Entanglement entropy in the semi-classical approximation as an observable for investigating shape phase transition in nuclei

In this paper, quantum phase transitions and nuclear structure were investigated based on quantum entanglement. One of the measures for entanglement between two bodies is the von Neumann entropy, which is considered a suitable criterion for examining entanglement. The entanglement entropy of s-d bosons within the framework of the Interacting Boson Model (IBM) is investigated using the consistent-Q formalism and semiclassical approximation. This research presents a method for deriving the entanglement entropy in the dynamical symmetry limits of the IBM, including transition regions between different shapes. By utilizing the entanglement effect, the quantum phase transition was described, and the entanglement behavior of s and d bosons was investigated in various regions of the Castan triangle. A method for determining entropy in the IBM model using the semiclassical approximation was presented. The results showed that entanglement entropy values are sensitive to phase changes and can be a powerful tool for detecting quantum phase transitions in nuclei.